$($a$)$ The density as a function of distance for the rod is given by $=B+Cx,$ where $B$ and $C$ are constants. What are the values of in $($:$\frac{g}{c}{m}^3\}$ and in $($:$\frac{g}{c}{m}^4\}?$

$B=,\frac{g}{c}{m}^3$

$C=,\frac{g}{c}{m}^4$

$($b$)$ Finding the total mass of the rod requires integrating the density function over the entire length of the rod. The integral is written as follows.

$m={\displaystyle \underset{\text{a}\text{l}\text{l}\text{m}\text{a}\text{t}\text{e}\text{r}\text{i}\text{a}\text{l}}{\overset{\phantom{}}{}}}dv={\displaystyle \underset{\text{a}\text{l}\text{l}x}{\overset{\phantom{}}{}}}Adx={\displaystyle \underset{0}{\overset{15\mathrm{.}0cm}{}}}(B+Cx)(8\mathrm{.}00c{m}^2)dx$

What is the total mass of the rod $($in $kg)?$

$kg$